Random action of compact Lie groups and minimax estimation of a mean pattern

This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics

Optimal functional supervised classification with separation condition

We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its worst-case excess risk over Sobolev spaces. These bounds are parametrized by a separation distance quantifying the difficulty of the problem, and are proved to be optimal (up to logarithmic factors) through matching minimax lower bounds. Using the recent works of [9] and [14] we also derive a logarithmic lower bound showing that the popular k-nearest neighbors classifier is far from optimality in this specific functional setting

Regional climate model emulator based on deep learning: concept and first evaluation of a novel hybrid downscaling approach

International audienceProviding reliable information on climate change at local scale remains a challenge of first importance for impact studies and policymakers. Here, we propose a novel hybrid downscaling method combining the strengths of both empirical statistical downscaling methods and Regional Climate Models (RCMs). In the longer term, the final aim of this tool is to enlarge the high-resolution RCM simulation ensembles at low cost to explore better the various sources of projection uncertainty at local scale. Using a neural network, we build a statistical RCM-emulator by estimating the downscaling function included in the RCM. This framework allows us to learn the relationship between large-scale predictors and a local surface variable of interest over the RCM domain in present and future climate. The RCM-emulator developed in this study is trained to produce daily maps of the near-surface temperature at the RCM resolution (12 km). The emulator demonstrates an excellent ability to reproduce the complex spatial structure and daily variability simulated by the RCM, particularly how the RCM refines the low-resolution climate patterns. Training in future climate appears to be a key feature of our emulator. Moreover, there is a substantial computational benefit of running the emulator rather than the RCM, since training the emulator takes about 2 h on GPU, and the prediction takes less than a minute. However, further work is needed to improve the reproduction of some temperature extremes, the climate change intensity and extend the proposed methodology to different regions, GCMs, RCMs, and variables of interest

Adaptive Simulated Annealing with Homogenization for Aircraft Trajectory Optimization

International audienceIn air traffic management, most optimization procedures are commonly based on deterministic modeling and do not take into account the uncertainties on environmental conditions (e.g., wind) and on air traffic control operations. However, aircraft performances in a real-world context are highly sensitive to these uncertainties. The aim of this work is twofold. First, we provide some numerical evidence of the sensitivity of fuel consumption and flight duration with respect to random fluctuations of the wind and the air traffic control operations. Second, we develop a global stochastic optimization procedure for general aircraft performance criteria. Since we consider general (black-box) cost functions, we develop a derivative-free optimization procedure: noisy simulated annealing (NSA)